接触问题

It is the purpose of this paper to review the contact problems and some recent developments using BEM.

本文回顾了使用边界元法处理接触问题的情况及目前的研究进展，详细叙述了处理这类问题的理论方法及相应的公式，然后讨论了解决这类问题所采用的边界元法的步骤和各种数值方法，同时给出了的大量的有关接触问题研究的参考文献及作者近期的研究工作，并提出一些有待进一步研究的问题

When it is used to solve contact problems,multiplepairs of contact points can be updated in each iteration,other thansome methods such as Thail-Van de Panne method and Goldfarb-Idnani method,which update only one pair of contact points at eachiteration.

用拟有效集方法解接触问题，每次迭代可以更换一组接触点对而不是某些方法只能更换一个接触点对，因此大大提高了解接触问题的效率。

The discretized frictional contact problems can be reduced as a linear complementarity problem using parametric variational principle and parametric quadratic programming method. Then we can apply the algorithms proposed in this thesis to the solution of the contact problems.

利用参变量变分原理和参数二次规划法，离散后的接触问题可化为线性互补问题，之后，将第二、三章提出的互补问题算法应用到接触问题的数值求解中。

The real borehole axis is not an ideal straight line, but a helical line with arbitrary curvature, so the contact problem between the down-hole string and the borehole face is a kind of arbitrary contact nonlinear mechanics problem, which can not be solved by the common methods from material mechanics and structural mechanics.

实际的井眼轴线不是理想的直线，而是一条任意曲率的空间螺旋线，因此井下管柱和井壁的接触问题是一种随机接触的非线性力学问题，用一般的材料力学和结构力学方法是不能解决这类问题的。

In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution.

第2章，给出三维边界单元及边界元空间、有摩擦接触边界元问题的Sobolev空间，利用变分不等式证明了不变接触区和随载荷可变接触区两种情况下的接触边界元法矩阵方程解的存在唯一性，给出了准确解与边界元解的误差表达式，还证明了三维弹塑性摩擦接触问题凝缩矩阵解的存在唯一性，为三维弹塑性摩擦接触边界元法奠定数学基础。

And the frontal technique is adapted to solve the FE equations. The techniques are studied to deal with the large slip frictional contactproblems between a deflectable body with large deformation and a rigid bodywith flat or curved surface. A new algorithm is presented to resolve such contactproblems, including incremental displacement constraints and force constraints,and the modules are programmed. The performances of tire under static load invertical loading state and camber state are analyzed by this method. And theexperiments were carried out at the same condition as used in analysis process.

研究了大变形柔性体与具有平面及曲面外形刚性体之间的大滑动摩擦接触问题，提出了求解这类接触问题的位移增量约束和主动力增量约束处理方法；编制了大变形柔性体与具有平面及曲面外形刚性体之间的大滑动摩擦接触问题求解模块；利用本文提出的大滑移接触问题处理方法，分析了轮胎在径向静载和静态外倾加载条件下受力和变形，并对部分分析结果进行了试验验证，验证结果表明，本文提出的位移增量约束和主动力增量约束处理接触问题的方法是正确可靠的，而且具有精度高、收敛性好、收敛速度快的优点。

Nevertheless, in these aPproaches the contact intethee are charactered sboly edstiffeess K. and K.' which is not PerfeCt and rigorous in thc vitw of solidmechanics and rather rough for the description of the behavior of the iDtfores. Incollbet, taken as a contact Problem, the principal chatrs of the iDtCthees can bereflected: the cbntact inifore is of shear strength Which imPlies tha a genericpair of contact points on the inidse will displace coincidentally if the tangentialfbrce at this POint has not reahed the 1imit resistance, else, relative s1ide betwee the\ points will occur along the tangental direction.

本论文在对这两种方法进行认真的分析后，说明它们对不连续面的描述并不合理，也无法反映出不连续面的主要力学特性，同时指出，将带有不连续面的岩土工程问题作为接触问题计算更为合理，它可将不连续面受力变形的主要特点反映出来，即：(1)接触面具有相应的&抗剪强度&，即当接触面上某一点处的切向应力小于该点处的抵抗强度时，点对共同变形；达到强度时，则沿切向发生相对滑动；(2)在整个变形过程中，发生接触的变形体不能相互侵入。

FEMOL is systematically applied to various moving boundary problems, including: membranes contact with rigid foundation, shape optimization of cross-sections of elastic torsional bar, seepage through a dam with a free surface, Mindlin-Reissner plates contact with rigid foundation, free Mindlin-Reissner plates on tensionless

三、将有限元线法分析推广应用到了一系列的动边界问题中，包括：薄膜接触问题，弹性扭转杆的截面优化问题，自由液面的稳定渗流问题，中厚板理论与刚性地基的接触问题，无拉力Winkler地基上自由中厚板问题，理想弹塑性扭转问题，理想弹塑性Ⅲ型裂纹问题。

Based on the contacting characteristics of the surfaces in MEMS, we use the continuum contact mechanics modeling and fracture mechanics concepts to give a closed-form solution for the adhesion of the flat-ended wedges, including the atomic pressure distribution, the variations of the contact area and air gap with the load.

基于MEMS表面的接触力学特点，本文运用连续介质接触力学及断裂力学方法，研究了平底锥冲头的粘着接触问题，给出了接触区的原子压力分布、接触面积和表面间隙随载荷变化的封闭解。

Aimed at all kinds of damage phenomena in the sleeve usage of oil-film bearing in the backup roll of Baoshan 1580 hot strip mill,during the process of elastic conjunction between sleeve and rollneck,deformation and load properties are quantitatively analyzed by boundary element method for 3D elastic and plastic contact problems.

针对宝钢1580热连轧机精轧机组支承辊油膜轴承锥套使用中存在的各类损伤问题，利用三维弹塑性接触问题边界元法定量分析了轧机油膜轴承锥套与轧辊辊颈过盈装配过程中的变形和载荷特性，得出了装拆过程中不同的胀型压力和轴向推力条件下锥套接触压力延母线方向的变化规律，同时锥套端部和密封槽附近接触压力峰值的存在是加速锥套损伤及降低其使用寿命的重要原因。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。